Random Thoughts on the Universe

Tuesday, November 09, 2010

Online Roulette Scheme...

We normally don't comment on internet get-rich-quick schemes, but this one caught our attention because it claims to mathematically guarantee a profit.

The setup is that you use an online casino to play roulette. You start by selecting a colour - say Red - and betting $1. If you win, you gain $1 and repeat the process. If you lose, then you double your bet to $2 so that if you win you gain $2 creating a net profit between the two spins of $1. If you lose, you double again to $4 so that a win again creates a net profit of $1 over all the spins. So everytime you win, you increase your total profit by $1 and the losses are balanced out by the next win. They usually add a comment about how the probability of losing 8 times in a row is only 0.5% so you are certain to win sometimes.

It is complete bunk.

Unfortunately a lot of otherwise intelligent people fall for this because it seems to be mathematically certain that you will eventually win and that you can keep winning until you quit playing. But look closer...

On the first spin you have an equal chance of winning or losing $1, so your average profit is $0. If you win, then the second spin is the same, with an average profit of $0. Suppose you lost the first spin, and then bet $2. Once again, you have an equal chance of gaining or losing that $2 and so the average winning is still $0. This will be true no matter how much you bet and how often - you can always expect to just break even.

Consider the odds for the first 3 rounds. The probability of 3 wins is about 12.5% and you gain $3. The probability of three losses is the same, and you lose $7. The probability of winning the first time and losing the next two is also the same, with a loss of $2 while losing once and then winning twice gives a profit of $2. You might win twice and lose the third, giving you a net profit of $1, but if you lose twice and win the third then you get only a $1 profit. Add up all the possible runs of three rounds, and you find again that you only break even.

It is true that the odds of losing 8 times in a row are small - only 0.5% or so. But if you follow this method, that run of losses will cost you $500! The odds of winning 8 times in a row are also 0.5%, and following this scheme you gain $8. So you have an equal chance of winning $8 or losing $500 - is that really a good bet?

Of course breaking even is not so bad, except the game described here is not exactly the way roulette is played in most online casinos. Usually there is a small probability of neither black nor red, and in that case you always lose. And that small loss will eventually take all the money you started with...

That is certainly no way to make a fortune!

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